Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 Articles in Press 2025 03 08 On compact pseudo-Riemannian manifolds admitting Killing vector fields 5695 10.22060/ajmc.2025.23742.1297 EN Reza Mirzaie Department of Pure Mathematic, Faculty of Science, Imam Khomeini International University, Qazvin, Iran 0000-0002-9480-0222 Journal Article 2024 12 09 We prove some theorems about the Killing vector fields on compact and connected pseudo-Riemannian manifolds. Among other results, we present a relationship between curvature of a compact pseudo-Riemannian manifold $M$ and existence of Killing vector fields on $M$. Pseudo-Riemannian manifold Killing vector field Lorentzian manifold